Modular Math

Algebra

Algebra printed booklet
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Algebra

Release Date: October 19

Welcome to Algebra! This unit of Modular Math is designed for students in Grades 3–9. In Foundations, students explore puzzles, patterns, basic equations, and problem-solving. As they progress, they work with variables, decipher codes, graph ordered pairs, simplify expressions, combine like terms, solve for unknowns, and explore radicals and fractions. By Step 6, students tackle linear and nonlinear equations, absolute values, polynomial operations, graphing, and quadratic functions.

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Modular Math Algebra

These are the main books in print and you will need one per student. Each step lasts about 5 weeks and contains a grade equivalent of content related to that topic. Spiral review is built in to all our levels as we explore multiple operations.

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Scope and Sequence

Check out the scope and sequence for this unit.

Decorative Arrow
  • Finish the pattern
  • Notice patterns
  • Recognizing patterns helps us predict what comes next
  • Try identifying what is happening and what repeats
  • Practice completing color patterns
  • Draw shapes to fill in what is missing in the pattern
  • Create your own pattern
  • Bible: 1 Corinthians 14:33
  • God brings order, not chaos
  • Missing numbers
  • Identify the rule to predict the way numbers are changing on a number line
  • Count up by 1, 2, and 5
  • Determine the rule that each number line follows and fill in the missing numbers
  • Create your own number line
  • Bible: Hebrews 13:8
  • God does not change
  • What is equal?
  • Equal means the same; not equal means different
  • Visualize equal and not equal on a scale
  • Make your own equal and not equal comparison
  • Practice determining if pairs of images are equal or not equal
  • Fill in the blank with equal or not equal
  • Write the missing number
  • Equal or not equal word problem
  • Bible: 1 Samuel 16:7
  • The Lord does not see as man sees
  • Introduction to equations
  • Understand word problems as equations
  • Identify the correct operation needed in an equation
  • Practice filling in the missing numbers to complete the equation
  • Create a number sentence from word problems
  • Create a word problem from a number sentence
  • Bible: Proverbs 2:2
  • God gives the ability to learn and understand
  • Missing addends
  • Using inverse operations to make fact families
  • Try identifying the equation from the word problem
  • Practice rewriting the problem to identify the missing part
  • Bible: Isaiah 30:21
  • God guides us when things seem missing in our lives
  • Missing numbers in subtraction
  • Defining minuend - subtrahend = difference
  • Try deciding if addition or subtraction should be used
  • Practice finding the missing minuend
  • Practice finding the missing subtrahend
  • Write a number sentence to represent the situation and solve it to find the missing number
  • Bible: 1 Corinthians 3:11
  • Jesus Christ is our foundation
  • Missing multipliers
  • Learn ways to find the missing multiplier: listing facts, skip counting, repeated addition, and drawing pictures
  • Try filling in the blanks of the number family
  • Try writing a multiplication equation to match the situation
  • Answer questions to determine the answer to the word problem
  • Bible: Matthew 6:8
  • Your Father knows what you need
  • What's the rule?
  • Identify patterns in a table
  • Practice using the rule listed to fill in missing numbers
  • Practice reading a table to answer questions
  • Practice completing a table
  • Practice determining the rule
  • Bible: Psalm 119:11
  • I have stored up your word in my heart
  • Two-step equations
  • Do one thing at a time working from left to right
  • Try filling in the blanks to solve each step
  • Practice solving equations one step at a time
  • Practice writing an equation to match the question
  • Create a word problem from an equation
  • Bible: Isaiah 41:10
  • God is with us in every step
  • Picture puzzles
  • Use symbols to represent numbers and solve problems
  • With a given key, try replacing the symbols with its number and rewrite the equation
  • Practice using clues to figure out the number each symbol stands for
  • Bible: James 1:5
  • God does not leave us to figure out life on our own
  • Identifying and extending patterns
  • Focus on how numbers are changing to determine the rule of a number pattern
  • Once you know the rule, you can continue the pattern
  • Practice filling in the blanks by following the rule listed
  • Practice finding the rule for each pattern and then fill in the blank
  • Bible: Proverbs 4:18
  • Understanding grows over time
  • Pascal's triangle
  • Each row begins and ends with 1
  • Numbers in each row are found by adding the two numbers adjacently above them
  • Practice finding the rule and filling in the blanks of the diagonal line
  • Find the sum of each row in Pascal's triangle
  • Identify the rule in the sums of Pascal's triangle
  • Bible: Psalm 147:5
  • God's understanding has no limits
  • Properties of addition
  • Identity, commutative, and associative
  • Try identifying the property shown
  • Practice combining properties to show the commutative property
  • Practice breaking apart equations to show the associative property
  • Bible: Romans 8:28
  • God works all things together for good
  • Properties of multiplication: identity, commutative, associative, and distributive
  • Try labeling the equation with its property name
  • Practice rewriting the expression to show the given property
  • Create your own example of each property
  • Bible: 2 Corinthians 5:17
  • Our identity changes when we choose to follow Christ
  • Simplifying expressions
  • When there is no equal sign, we simplify it
  • Try rewriting the given expression in words
  • Practice simplifying expressions working from left to right
  • Write an expression from the word problem given and simplify
  • Try writing your own word problem
  • Bible: 1 Timothy 6:8
  • We should be content without needing to add more to what we already have
  • Adding positive and negative numbers
  • Adding two negative numbers produces a negative
  • Adding two numbers with different signs: keep the sign of the larger number
  • Try adding the given digits
  • Circle the sign to show if the sum will be positive or negative
  • Practice finding the sum
  • Work with expressions with more than two numbers
  • Write you own addition problem with positive and negative numbers and have someone else solve it
  • Bible: Luke 6:27
  • Doing something negative back to someone who has upset us doesn’t result in a positive outcome
  • Comparing numbers
  • Comparison: greater, less, or equal
  • Simplify before comparing
  • Try comparing given expressions
  • Practice simplifying before comparing
  • Practice comparing negative numbers
  • Create expressions from a word problem and compare
  • Bible: Matthew 22:37
  • Love the Lord your God
  • Missing numbers in addition and subtraction
  • Learn when to use addition and when to use subtraction
  • Explain when to use addition versus subtraction to find the missing number
  • Work left to right to find the missing number
  • Write an equation from the word problem and solve
  • Bible: Matthew 7:7
  • God is not hiding from us
  • Missing factors
  • Find using division as the inverse operation
  • Try rewriting the multiplication equation as division to solve
  • Practice solving for the missing factor
  • Create your own equation and solve
  • Bible: John 10:10b
  • Christ came to give us life more abundantly
  • Representing an unknown
  • Use variables to represent unknown parts of an equation
  • Try rewriting equations with variables instead of blanks
  • Practice writing a variable equation to represent the word problem
  • Write equations using variables
  • Create word problems to match the given equation
  • Bible: 2 Peter 3:18a
  • We can grow in our faith
  • Working with sequences
  • Sequences: arithmetic and geometric
  • Sequences that are neither arithmetic nor geometric
  • Try identifying the rule in the given sequence
  • Practice finishing the sequence after identifying the rule
  • Identify patterns in shapes and continue the sequence
  • Bible: Genesis 2:2
  • God rested on the seventh day
  • Patterns and codes
  • Use clues to determine the value of the symbol
  • Try simplifying expressions
  • Practice finding the value of each symbol
  • Decoding the equation to determine the value of the letters
  • Solve the math puzzle
  • Bible: Ephesians 4:16
  • God created each person with an important role to play
  • Balancing equations
  • Use mental math and inverse operation to make both sides of an equation equal
  • Try identifying the balanced equations
  • Practice filling in the missing part to balance the equation
  • Simplify one side of the equation first before solving the missing part
  • Create an equation from a word problem and solve for the missing part
  • Create your own balanced equations
  • Bible: Colossians 3:15
  • Peace brings balance to our lives
  • All about inequalities
  • Define variables
  • Inequality symbols: greater than, less than, greater than or equal to, less than or equal to
  • Try identifying the numbers that could be included in the solution
  • Practice writing inequalities to match the statement
  • Represent inequalities on a number line
  • Bible: 1 Corinthians 10:31
  • Do all to the glory of God
  • Algebraic properties
  • Addition and multiplication properties: identity, commutative, associative, inverse, and distributive
  • Name the property by the equation shown
  • Fill in the blanks to demonstrate the property named
  • Solve using the distributive property
  • Write an equation to represent the situation listed and name the property being demonstrated
  • Bible: Mark 16:15
  • Proclaim the gospel to the whole creation
  • Positive and negative numbers
  • Add and subtract integers
  • Multiply and divide integers
  • Try to determine if the solution will be positive or negative
  • Practice solving the equations, paying attention to determine if the solution should be positive or negative
  • Bible: Proverbs 4:23
  • Keep your heart with all vigilance
  • Order of operations
  • PEMDAS: parentheses, exponents, multiplication or division, addition or subtraction
  • Try to highlight the first step that should be solved in the given expressions
  • Simplify the expressions using order of operations
  • Bible: James 1:19b
  • Practice patience and self–control
  • Solving for variables
  • Use inverse operations to isolate the unknown variable before solving
  • Multiplication can be written different ways: x, dot, or parentheses
  • Division can be written different ways: division symbol or fraction
  • Try checking the answer by plugging the solution back into the original equation
  • Practice using inverse operation to isolate the variable
  • Write equations from word problems
  • Bible: Proverbs 4:25
  • Let your eyes look directly forward
  • Input and output tables
  • A set rule applied to all values input into the table produces an output to each value
  • Study the inputs and outputs to determine the rule if it is not given
  • Use the given rule to determine the outputs in the table
  • Determine the rule from the given table
  • Find the error in the table
  • Complete the table by applying the given rule
  • Bible: Psalm 19:1
  • The heavens declare the glory of God
  • Coordinate grids
  • Parts of a grid: x–axis, y–axis, and origin
  • Naming points as ordered pairs
  • Plot ordered pairs on the coordinate grid
  • Determine an ordered pair by how you move on the grid
  • Describe how to move on the grid based on the ordered pair given
  • Identify the grid point by directions of how to move
  • Label each coordinate by its ordered pair
  • Bible: Proverbs 16:9
  • The Lord establishes His steps
  • Sequencing with terms and periods
  • Parts of a sequence: term and period
  • Identify repeating patterns, terms, and periods in a sequence
  • Write a sequence using the given terms and periods
  • Bible: 1 Thessalonians 5:16–18
  • Rejoice always, pray without ceasing, give thanks in all circumstances
  • Triangular numbers
  • Define what numbers are triangular
  • Complete the sequence to determine the next triangular numbers in the set
  • Find the difference in the previous two terms and add one to determine the number to add to find the next term
  • Identify the triangular numbers
  • Bible: Proverbs 9:10
  • The fear of the Lord is the beginning of knowledge
  • Algebraic expressions
  • Define algebraic terms: variable, coefficient, constant, and terms
  • Types of expressions: monomial, binomial, and trinomial
  • Label parts of a trinomial expression
  • Identify and circle the terms in an expression
  • Explain what is happening to each term in an expression
  • Bible: Proverbs 3:5–6
  • Trust in the Lord with all your heart
  • Combining like terms
  • Define like and unlike terms
  • Simplify expressions by combining like terms
  • Highlight the terms that can be combined in each expression
  • Check if an expression can be simplified by combining like terms
  • Combine the highlighted terms in the expression
  • Determine if the expression has been simplified correctly
  • Bible: 1 Corinthians 14:33
  • God is not a God of confusion
  • Evaluating expressions
  • Substitute the given value for each time that variable appears in an expression
  • Simplify using PEMDAS
  • Rewrite the expression, substituting the variable
  • Hightlight the first step you would complete in the expression according to PEMDAS
  • Evaluate the given expressions
  • Bible: Ephesians 6:11
  • Put on the whole armor of God
  • Solving equations
  • Use inverse operations to isolate the variable
  • Substitute the given value for the variable and solve the equation
  • Identify the inverse operation needed to isolate the variable
  • Check your answer using substitution
  • Solve multistep equations using inverse operations
  • Bible: Hebrews 12:1b
  • Let us lay aside every weight
  • Word problems with variables
  • Clue words help show operations needed to solve
  • Write an expression representing the word problem given
  • Highlight clue words and determine the operation needed to solve the word problem
  • Analyze the word problem and write the equation needed to solve it
  • Solve the word problem using all the learned steps
  • Bible: Psalm 19:1
  • The heavens declare the glory of God
  • Functions
  • Define function in relation to inputs and outputs
  • Determine a function (or rule) based on the inputs and outputs in a table
  • Apply the function to the input values in a table to determine the outputs
  • Bible: Galatians 6:7
  • One reaps what he sows
  • Solving and graphing inequalities
  • Inequalities represent a set of numbers
  • Represent an inequality number set on a line
  • Write inequalities from a situation
  • Use words to explain what an inequality represents
  • Solve inequalities
  • Graph inequalities on a number line
  • When to flip the inequality sign
  • Bible: Ephesians 3:20
  • God is never limited
  • Graphing linear functions
  • Data from an input/output table can be written as ordered pairs
  • Ordered pairs from linear functions form straight lines on a coordinate plane
  • Fill in the missing output values by applying the given function to the input values
  • Fill in an input/output table from the coordinates on a graph
  • Graph the coordinates from the ordered pairs in an input/output table
  • Bible: Psalm 103:12
  • God removes our transgressions from us
  • Algebraic notations
  • Simplify equations using shortcuts
  • Define coefficients and exponents
  • Rewrite expressions in algebraic notation
  • Write algebraic expressions in words
  • Find the rule in the table and write it as an algebraic notation
  • Bible: Matthew 22:37–40
  • Love God and love others
  • Symbols of inclusion
  • Symbols: parentheses, brackets, and braces
  • Work from inner most symbols outward
  • Rewrite expressions using different grouping symbols
  • Simplify expressions
  • Bible: 1 Samuel 16:7b
  • The Lord looks on the heart
  • Order of operations
  • Acronyms: PEMDAS and BOMDAS
  • Show understanding of why multiplication does not always come before division
  • Use order of operation to simplify expressions
  • Use of parentheses with negative numbers
  • Bible: Matthew 6:33
  • Seek first the kingdom of God
  • Solving algebraic equations
  • Find missing values using inverse operation in the reverse order
  • Explain what operations are undone in each step to find the value of the variable
  • Plug the value of the variable back into the original equation
  • Isolate the variable to solve the equation
  • Use order of operations and isolating variables to solve the equations
  • Bible: 1 John 1:9
  • Because of Christ, the penalty of our sins can be undone
  • Equations with fractions
  • Multiply to isolate the variable in a fraction
  • With multistep equations, work in reverse order of operations to isolate the variable
  • Remove the variable from the denominator before using inverse operation to isolate
  • Solve multistep equations where the variable is in the denominator
  • Bible: James 1:2–3
  • Count it all joy when you meet trials
  • Evaluating expressions with multiple variables
  • Replace variables with given values to simplify the expression
  • Variable locations: whole numbers, fractions, and exponenets
  • Fill in the missing piece of each expression and simplify
  • Bible: 2 Corinthians 5:20a
  • Christians are called to represent Jesus
  • Working with two unknowns
  • Use two related equations in a system to solve for unknow variables in each equation
  • Methods: substitution and elimination
  • Practice isolating one variable
  • Plug the ordered pair into the original equations to determine if they are a solution to the system
  • Solve systems by substitution
  • Solve systems by elimination
  • Bible: Romans 12:6
  • God created people with different gifts
  • Transforming equations
  • Rearrange a formula to find the unknown value
  • Transform the formula to solve for the missing measurement
  • Rewrite the formula to solve for different variables
  • Transforming formulas helps solve for missing measurements in real-world situations
  • Bible: Hebrews 13:8
  • God does not change
  • Unit rates
  • Make comparisons to show rate per individual unit
  • Keep the relationship proportional
  • Solve using cross-multiplication
  • Determine if the scenario is rate or unit rate
  • Find the unit rate for the given example
  • Keep the relationship proportional and cross-multiply to solve for the missing amounts
  • Bible: Ephesians 5:15–16
  • Make the best of your time
  • Slope-intercept form
  • Understand the slope on a coordinate plane
  • Linear equations written in slope-intercept form
  • Learn to graph an equation from slope-intercept form
  • Identify the slope and y-intercept from the equation
  • Explain how a positive slope moves versus a negative slope
  • Plot the given equations on a coordinate plane
  • Bible: James 4:14b
  • You are a mist that appears for a little time
  • Laws of exponents
  • Multiply powers, divide powers, power of a product, power of a quotient, exponent of one, zero exponent, power raised to a power, and negative exponent
  • Try to name the exponent rule to the given expression
  • Practice simplifying each expression
  • Bible: 1 Corinthians 3:11
  • Jesus Christ is our foundation
  • Simplifying algebraic expressions
  • Learn the order of solving
  • Try combining like terms in expressions
  • Practice using the distributive property to remove parentheses
  • Multiply the expression using the FOIL method
  • Simplify the expression in a multi-step process
  • Bible: 1 Timothy 6:6
  • Godliness with contentment is great gain
  • Factoring expressions
  • Greatest common factor (GCF)
  • Steps to factoring expressions
  • Try finding the GCF
  • Practice factoring given expressions
  • A negative GCF works the same way as a positive one, but it flips the signs inside the parentheses
  • Bible: Proverbs 3:5–6
  • Trust in the LORD with all your heart
  • Solving equations with square roots
  • Operation: multiply a number by itself
  • Inverse operation: take the square root
  • The squared term must be isolated first
  • Try using your calculator to find the square root of the given numbers
  • Practice isolating the variable in a two-step equation before finding the square root
  • A cubed number is multiplied by itself three times
  • Bible: 2 Corinthians 9:8
  • God provides what is needed for each moment
  • Radical equations
  • Inverse operations: square and square root, cube and cube root
  • Try to see if the solution value makes the equation true
  • Practice filling in the blanks to complete the equation
  • Explain the steps to isolate and solve for x in the given equation
  • Practice isolating the square root and then solving
  • Bible: John 14:6
  • Jesus is the way
  • Solving fractional equations
  • Quick review on fraction rules
  • Isolate using the inverse operation
  • What to do when denominators are the same or different
  • Try solving each given equation
  • Practice combining fractions before you solve
  • Combine the fractions and solve for the unknown
  • Describe what is happening in each step of the solved equaiton
  • Practice solving equations
  • Bible: Hebrews 12:1
  • Letting go of distractions in life helps us see more clearly
  • Proportional relationships
  • Occur when one quantity grows in a constant rate compared to another quantity
  • The constant of proportionality
  • Try to find the unit rate by dividing
  • Practice using the formula for speed to answer the word problem
  • Practice cross multiplication
  • Set up proportions and solve for missing variables
  • Bible: James 2:17
  • Faith without works is dead
  • Solving simultaneous equations (part 1)
  • Compare by finding where two equations are equal to one another
  • Solve using substitution or elimination
  • Determine if two equations are simultaneous equations
  • Practice solving for the equations using substitution and elimination
  • Bible: Hebrews 13:8
  • God is our constant
  • Solving simultaneous equations (part 2)
  • Use ordered pairs to graph simultaneous equations
  • Practice using a graph to solve two simultaneous equations
  • Practice filing out a table to find the y-values to the ordered pairs
  • Plot the ordered pairs on a graph
  • Bible: Hebrews 10:24
  • Our words and actions should encourage others
  • Linear inequalities
  • Multiplying or dividing by a negative reverses the inequality symbol
  • Graph an inequality with two unknown variables
  • Try simplifying and solving inequalities
  • Graph and shade an inequality
  • Bible: Romans 12:2
  • Be transformed by the renewal of your mind
  • Properties of equality
  • Three properties: reflexive, symmetric, and transitive
  • Try naming the property demonstrated
  • Practice writing reflexive and transitive equations
  • Determine true or false statements and rewrite false statements to become true
  • Write your own example of each property
  • Bible: Galatians 3:28
  • God sees each person as equally valued and loved
  • Types of linear equations
  • Identity, conditional, and inconsistent
  • Label the equation type from examples
  • Practice simplifying and labeling each type of equation
  • Bible: Hebrews 13:8; Jesus is the same
  • John 15:5; Apart from Me you can do nothing
  • 1 John 1:5–6; We cannot have fellowship with Him while we walk in darkness
  • Literal equations
  • Steps to rearranging the equation
  • Try writing the inverse operation to isolate the variable
  • Practice rewriting the equation to isolate the given variable
  • Bible: Luke 5:16
  • Sometimes isolating allows you to draw close
  • Solving multistep equations
  • Simplify and combine like terms until the variable is isolated
  • Follow the steps to solve the equation
  • Practice solving the problems to find the variable
  • Evaluate if the distributive property makes the equation clearer or more complicated
  • Practice combining like terms
  • Try using the distributive property, combining like terms, and using inverse operations in the same equation
  • Bible: Psalm 119:105
  • God's word is a light to our lives
  • Absolute value
  • Refers to distance from zero
  • Always positive
  • Usually has two solutions
  • Practice setting up two equations and solve for the variable
  • Try writing absolute value equations from word problems
  • Bible: Romans 8:38–39
  • Our value is secure because it comes from God
  • Polynomial operations
  • Defined: an algebraic expression made of terms with numbers, variables, and exponents
  • Try identifying parts of a polynomial
  • Practice adding, subtracting, and multiplying polynomials
  • Bible: Daniel 2:21–22
  • God gives wisdom and knowledge
  • Functional relationships
  • Rule: one input gives exactly one output
  • Define domain and range
  • Practice simplifying a function with the given value
  • Practice using the given function to complete a table
  • Use the function given to complete your own table
  • Write an equation to represent the table shown
  • Bible: Matthew 28:19–20
  • Jesus has called us to a task
  • Linear functions and graphing
  • Define the slope of a line
  • Graph from an equation
  • Find the equation from a graph
  • Try finding the y-intercept (b) from the given variables
  • Practice finding the slope (m) by using a formula
  • Practice graphing the line
  • Bible: Psalm 147:5
  • God's understanding is beyond measure
  • Nonlinear equations
  • Kinds of graphs: cubic, absolute value, exponential, and radical
  • From chosen x-values, find y-values and use those points to create a graph
  • Try completing a table using a given function
  • Practice identifying the kind of graph a given function will produce
  • Practice plotting points on a graph
  • Bible: Romans 8:28
  • God knows the whole picture
  • Quadratic functions
  • These create a curved shape called a parabola when graphed
  • Changing the coefficient of x² transforms the parabola
  • Try using the rule to complete the ordered pairs
  • Practice finding the points and graphing the quadratic function
  • Bible: Isaiah 43:1b–2
  • God does not leave when life dips